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A General Computational Treatment Of The Comparative Carol Friedman" Courant Institute of Mathematical Sciences New York University 715 Broadway, Room 709 New York, NY 10005 Abstract We present a general treatment of the com- parative that is based on more basic linguistic elements so that the underlying system can be effectively utilized: in the syntactic analy- sis phase, the comparative is treated the same as similar structures; in the syntactic regular- ization phase, the comparative is transformed into a standard form so that subsequent pro- ceasing is basically unaffected by it. The scope of quantifiers under the comparative is also in- tegrated into the system in a general way. 1 Introduction Recently there has been interest in the devel- opment of a general computational treatment of the comparative. Last year at the Annual ACL Meeting, two papers were presented on the comparative by Ballard [1] and Rayner and Banks [14]. Previous to that a compre- hensive treatment of the comparative was in- corporated into the syntactic analyzer of the Linguistic String Project [15]; in addition the DIALOGIC grammar utilized by TEAM [9] also contains some coverage of the compara- tive. An interest in the comparative is not sur- prising because it occurs regularly in lan- *This work was supported by the Defense Ad- vanced Re.arch Projects Agency under Contract N00014-8.5-K-0163 from the Office of Naval Research. The author's current addr¢~ is: Center for Medical Infornmti~, Columhia~Pre~byterian Medical Center, Columbia University, 161 Fort Waahington Avenue, Room 1310, New York NY 10032. guage, and yet is a very difficult structure to process by computer. Because it can occur in a variety of forms pervasively throughout the grammar, its incorporation into a NL system is a major undertaking which can easily ren- der the system unwieldy. We will describe an approach to the computational treatment of the comparative, which provides more general coverage of the comparative than that of other NLP Systems while not obscuring the underly- ing system. This is accomplished by associat- ing the comparative with simpler, more basic linguistic entities so that it could be processed by the system with only minor modifications. The implementation of the comparative de- scribed in this paper was done for the Pro- re,8 Question Answering System [8] 1 (referred to hereafter as Proteus QAS), and should be adaptable for other systems which have sim- ilar modules. A more detailed discussion of this work is given in [7]. 1.1 The Problem The comparative is a difficult structure to pro- cess for both syntactic and semantic reasons. Syntactically the comparative is extraordinar- ily diverse. The following sentences illustrate a range of different types of comparative struc- tures, some of which resemble other English structures, as noted by Sager [15]. In the ex- amples below, sentences with the comparative that resemble other forms are followed by a 1 The treatment of the comp~'ative in the syntac- tic analysis component was adapted from a previous implementation done by this 8uthor for the Linguistic String Project [15]. 161 sentence illustrating the similar form: conjunction-like : la.Men eat more apples than oranges. lb.Men eat apples and oranges. 2a.More men buy than write books. 2b.Men buy and write books. 3a. We are more for than against the plan. 3b. We are for or against the plan. 4a.He read more than 8 books. 4b.He read ~ or 3 books. wh-relative-clanse-like : 5a.More guests than we invited visited us. 5b.Guests that we invited visited as. subordinate and adverbial : 6a.More visitors came than was ezpected. 6b. Visitors came, which was ezpected. 7a.More visitors came than usual. 7b.Many t~sitors came as usual. Special Comparative Constructions : 8.A taller man than John visited us. 9. John is taller than 6 ft. 10. A man taller than John visited us. 11.He ran faster than ever. The problems in covering the syntax of the comparative are therefore at least as complex as the problems encountered for general coor- dinate conjunctions, relative clauses, and cer- tain subordinate and adverbial clauses. Incor- porating conjunction-like comparatives into a grammar is particularly difficult because that structure can occur almost anywhere in the grammar. Wh-relative-clause-like compara- tives are complicated because they contain an omitted noun where the omission can oc- cur arbitrarily deep within the comparative clause. The comparative is difficult to process for semantic reasons also because the comparative marker can occur on different linguistic cate- gories. Adjectives, quantifiers, and adverbs can all take the comparative form, as in: he is taller than John, he took more courses than John, and he ran faster than John. There- fore the semantics of the comparative has to be consistent with the semantics of different linguistic categories while retaining its own unique characteristics. 2 The Underlying System Proteus QAS answers natural language queries relevant to a domain of student records. It is highly modular and contains fairly standard components which perform: 1. A syntactic analysis of the sentence us- ing an augmented context-free grammar consisting of a context-free component which defines the grammatical structures, a restriction component which contains welbformedness constraints between con- stituents, and a lexicon which classifies words according to syntactic and seman- tic categories. 2. A syntactic regularization of the anal- ysis using Montague-style compositional translation rules to obtain a uniform operator-operand structure. 3. A domain analysis of the regularized structure to obtain an interpretation in the domain. 4. An analysis of the scope of the quanti- tiers. 5. A translation to logical form. 6. Retrieval and answer generation. The syntactic analyzer also covers general coordinate conjunction by containing a con- junction metarule mechanism which automat- ically adds a production containing conjunc- tion to certain context-free definitions. 3 The Syntactic Analysis of the Comparative In Section 1.1 it was shown that the com- parative resembles other complex syntactic structures. This observation suggests that the comparative could be treated as general coordinate conjunctions, wh-relative clauses, and certain subordinate and adverbial clauses 162 by the syntactic analysis component of the system. If the system can already handle these structures, the extension for the compar- ative is straightforward. This approach has the advantage of utilizing the system's exist- ing machinery to process comparative struc- tures which are very complex and diverse; in this way a minimal amount of effort re- sults in extensive coverage. For example, to cover conjunction-like comparative structures, the production containing possible conjunc- tions was modified to include than; to include relative-clause-like comparatives, the produc- tion containing words which can head rela- tive clauses was also modified to include than. Analogous minor grammar changes were made for the other types of similar structures shown above. Using this approach, a comprehen- sive comparative extension was obtained by a trivial modification of only a small number of grammar productions. Thus, a conjunction-like comparative struc- ture such as Sentence la. in Section 1.1 would be analyzed as consisting of an object which contains a conjoined noun phrase more apples CONJ 0 oranges where the value of CONJ is than, and where a quantifier phrase similar to more has been omitted which occurs with oranges. A relative-clause type of compara- tive structure such as Sentence 5a. would be analyzed as a relative clause than we invited 0 adjoined to more guests. Those construc- tions that are unique to the comparative, as shown in Sehtences 8 through 11, have to be uniquely defined. For example, the compara- tive clause in Sentence 8 is defined as a clause where the predicate is omitted, whereas the comparative clause in Sentence 9 is defined as a measure phrase. Although the comparative syntactically re- sembles other structures, this type of similar- ity does not carry over to the underlying struc- ture or to the semantics of the comparative, as will be discussed shortly. There are also some syntactic differences be- tween the comparative and the structures it resembles. For example, the comparative has zeroing patterns that are somewhat different from those associated with conjunctions: + John slept more than Mary [slept]. - John slept and Mary [slept]. The comparative constructions also have scope marker constraints that are not appli- cable to non-comparative structures. These differences are handled by special add-on con- straints that specifically deal with the com- parative, and do not interfere with the other restrictions. The treatment of the comparative marker is complicated because it can occur in a large number of different locations in the head clause 2, as illustrated by a few examples be- low: He wanted to travel to more coun- tries than he was able to. He is taller than Mary. He ate 3 more apples than Mary did. He ate more in the fall than in the winter. Because the comparative marker can occur in such a variety of locations and also be deeply embedded in the head clause, it cannot be con- veniently handled in the BNF component of the grammar. Instead, the constraint com- ponent deals with this problem by means of special constraints that assign and pass up the comparativ e marker; other constraints test that the comparative clause is in the scope of the marker. 4 Underlying Structure Basically, linguists such as Chomsky [3,4], Bresnan [2], Harris [10], and Pinkham [13] agree on fundamental aspects concerning the underlying structure of the comparative. They regard its underlying structure as con- sisting of two complete clauses where informa- tion in the comparative clause which is iden- tical to information in the head clause is re- quired to be zeroed. Harris' work is particularly suitable for computational purposes because he claims that one underlying structure is the source of 2This phrase was used by Bresnan [2] to refer to the clause of the comparative that contains the com- parative marker. 163 all comparative forms. We modified his in- terpretation somewhat to obtain a more con- venient form for computation. In our ver- sion, the underlying structure contains a main clause where the comparison is the primary relation; each quantity in the relation con- tains an embedded clause specifying the quan- tity being compared. An example of this form is shown below for the sentence John ate more apples than Mary, which resembles a conjunction-like comparative structure where the verb phrase has been omitted: Nx [John ate Nx apples] > N2 [Mary ate N2 apples] This form is also appropriate for all the different comparative forms shown in Sec- tion 1.1. For example, the underlying form for a relative-clause-like comparative, such as Sentence 5a. is: N1 [Nx guests visited us] > N2 [we invited N2 guests] The underlying form for a sentence such as a man taller than John visited us is slightly dif- ferent because the comparative structure it- self is embedded in a noun phrase. The main clause is a man visited us, and the compar- ative structure is a clause adjoining a man, whose underlying structure is: NI [the man is N1 tall] > N2 [John is N2 tall] The notion that there is one underlying form for all comparatives has important im- plications for a computational treatment: • Regularization procedures can be written to transform all comparative structures into one standard form consisting of a comparative operator and two complete clauses which specify the quantities be- ing compared. • In the standard form, each clause of the comparative operator is a simpler struc- ture which can be processed using basi- cally the usual procedures of the system. This means that further processing does not have to be modified for the compara- tive. This process can be illustrated by a simple ex- ample. When the sentence more guests than we invited visited us is regularized, a structure consisting of an operator connecting two com- plete clauses is obtained: (> (visited (er guests) (us)) (invited (we) (than guests))) The symbols er and than, shown above, roughly correspond to quantities being com- pared, and in subsequent processing they are each interpreted as denoting a certain type of quantity. Notice that each clause of the comparative is also in operator-operand form where generally the verb of a sentence is con- sidered the operator and the subject and ob- ject (and sometimes sentence adjunct phrases) are considered the operands z. Each of the two clauses can be processed in the usual manner provided that er and than are treated appro- priately. This will be described further in Sec- tion 5 which contains a discussion of semantics and the comparative. The regularization process was modified to be a two phase process. The first phase uses ordinary compositional translation rules to perform the standard regularization so that the surface analysis is transformed into a uni- form operator-operand form. The composi- tional regularization procedure is effective for fairly basic sentence structures but not for complex ones such as the comparative. The compositional rules associated with compara- tive structures only include labels categoriz- ing the type of comparative structure. The second phase, written specifically for the com- parative, completes the regularization process by filling in the missing elements, permuting the structures to obtain the correct operator- operand form, and supplying the appropriate quantifiers er and than to the items being comparativized. An example of this process is shown for the relative-clause type of com- parative in more guests than we invited visited as, where the comparative clause than we in- vited is analyzed syntactically as being a right adjunct modifier of guests. 3However, if the predicate is an ad~ectlvsl phrase, the adjective is considered the operator and the verb be the tense c~-rier. Thus, ignoring tense information, the regularized form of John is t611 is: (tall (John)). 164 Phase I: (visited (more guests (reln-than (invited (we) 0))) (us)) Phase 2: (> (visited (er guests) (us)) (invited (we) (than guests))) Another example is shown below for a conjunction-like comparative, such as John ate more apples than oranges: Phase 1: (ate (John) (conj-than (more oranges) (0 oranges))) Phase 2: (> (ate (John) (er apples) • (ate (John) (than oranges))) There are a few key points that should be made concerning the regularization proce- dures. The Montague-style translation rules could not readily be used to regularize the comparative constructions as they were de- fined in the context-free component. To use the rules, the grammar would have to be mod- ified substantially because the translation of the comparative is different and more com- plex than that of the structures it resembles. In particular, it would then not be possible to use the general conjunction mechanism to obtain coverage of that type of comparative structure. In the case of the usual relative clause, the regularized form is also substan- tially different from the regularized form of the relative-clause type of comparative shown above. For a typical relative clause, such as that we invited 0 in g.ests that we invited vis- ited us, the regularized form occurs as a clause embedded in the main clause as follows: (visited (guests (invited (we) 0)) (us)) The second important point is that be- cause of regularization further processing of sentences containing a comparative is signifi- cantly simplified and only minor changes are required specifically for the comparative. In Prote,s QAS, as well as other NLP Sys- tems, several other processing components are needed after syntactic regularization until the final result is obtained. Therefore a signifi- cant result of our approach is that subsequent components do not have to be modified for the comparative. As long as the underlying sys- tem can handle adjectives, degree expressions, quantifiers, and adverbs, the remainder of the processing of sentences with the comparative is basically no different than the processing of ordinary sentences because at that point the comparative is represented as being composed of fundamental linguistic entities. 5 Semantics of the Com- parative Semantically the comparative denotes the comparison of two quantities relative to a cer- tain scale. This interpretation is consistent with work in formal semantics ( [12,11], [6,5]), although our formalism is not the same. Since the comparative marker can occur with adjectives, quantifiers, and adverbs, we would like to integrate its semantic treat- ment with the semantics of those fundamen- tal linguistic categories and also remain true to the semantics and syntax of the compara- tive. This can be done by noting that once the comparative is regularized, the compara- tive marker becomes a higher order operator connecting two clauses and what remains of the marker within each clause functions as a quantitative phrase. For example, the regu- larized form for/s John taller than Mary is: (> (tall (DEG er) (John)) (tall (DEG than) (Mary)).) In this form er and than are each interpreted as a type of degree phrase that occurs with adjectives. In a question answering applica- tion such as that of Proteus QAS, each clause of the above form is equivalent to the regu- larized form of how tall is John, where how is also interpreted as a degree phrase modifying tall: (tall (DEG how) (John)) The interpretation of a sentence containing the comparative is therefore reduced to the interpretation of two similar simpler clauses, each containing an adjective operator and an 165 operand which is a degree phrase. Issues con- cerning the correct scale and criteria of com- parison for adjectives are non-trivial, but are generally not different from those issues con- cerning adjectives not being comparativized. For example, determining the scale and crite- ria that should be used to interpret is John more refiable than Jim raises similar issues to those for ho~a reliable is Jim. The semantic treatment of adverbs gener- ally parallels that of adjectives; the interpre- tation of quantifiers in the comparative form is also equivalent to the interpretation of cer- tain interrogatives. For example, the regular- ized form of did John take more courses than Mary consists roughly of the two clauses John took er courses and Mary took than courses, which is treated analogously to how many in how many courses did John take. 6 Quantifier Analysis An interesting problem involving the compar- ative concerns the scope of quantifiers when there is a higher order sentential operator such as the comparative. The problem is not dis- cussed much in the literature, but was dis- cussed by Rayner and Banks [14] when they described their treatment ofquantifiers for ev- eryone spent more money in London than in New York. The basic issue is whether the quantifier every in everyone should be given wider scope than the comparative itself, in which case it is applicable to both clauses of the comparative. Our approach addresses this problem in a general way by adding a prelimi- nary phase to the standard quantifier analysis. Our approach has several key features: • The replication of a quantified noun phrase does not lead to impossible scop- ing combinations, as frequently happens when these phrases are replicated for the purpose of obtaining a complete clause. • Our approach is applicable to all gen- eral higher order operators connecting two clauses. • The scope of quantifiers is determined in a late stage of processing so that corn- mittment is not done prematurely. • A procedure using pragmatics and do- main knowledge can easily be incorpo- rated into the system as a separate com- ponent to aid in scope determination. In Proteus QAS, the scope of quantifiers is determined subsequent to the regularization and domain analysis components in a manner similar to other NLP Systems, as described by Woods [16]. The basic quantifer analysis pro- cedure initially handled simple clauses, and therefore had to be modified to accommodate scope determination when a sentence contains a higher order operator such as a compara- tive or a coordinate conjunction. A prelim- inary quantifier analysis phase was added to find and label quantifiers which have a wider scope than the comparative. In addition, mi- nor modifications were made to the compo- nent which translates the regularized form to logical form, in order to handle the translation of wider scope quantifiers. Generally, in the case of the comparative, the criteria used for determining whether or not a quantifier should have a wider scope in- volves the location of the quantifier relative to the comparative marker in the surface form. Usually, a preference is given to the wider scope interpretation if the quantifier precedes the marker. Using this approach, the sen- tence everyone spent more money in London than in New York is first interpreted syntac- tically as consisting of two complete clauses, which are roughly everyone spent er money in London and everyone spent than money in New York. The semantics of each clause is interpreted the same as that of a simpler sen- tence how much money did everyone spend in London. The preliminary quantifier analysis phase prefers the reading where the scope of everyone is wider than the comparative opera- tor because everyone precedes more. The sen- tence is translated to logical form so that the quantified expression YX : person(X) occurs outside the comparative operator, and there- fore has scope over both c|auses of the com- parative. The interpretation is roughly: 166 VX:person(X)(>(spent (X) (er money) (in London)) (spent (X) (than money) (in New York))) A different scope interpretation is obtained for more students read than wrote a book, where the two clauses are er students read a book and than students wrote a book. The nar- row scope interpretation of a in a book is ob- tained because a follows more. In this case, the quantified expressions for each clause of the comparative are completely independent of the other. 7 Concluding Remarks We have presented a method for incorporat- ing general comparatives into a system with- out unduly complicating the system. This is done in the syntactic analysis component by treating the comparatives the same as simi- lar structures so that features of the syntac- tic analyzer that already exist may be uti- lized. The various comparative structures are then regularized so that they are in a stan- dard form consisting of a comparative opera- tor and two complete clauses that contain a quantity er or than which is interpreted by the semantic component as a quantity such as how, how many, or how much, as ap- propriate. A preliminary quantifier analysis component was added to determine whether a sentence containing a higher order operator has any quantifiers which have a wider scope than the operator, and to label those that do. The remainder of the processing is done as usual except for minor modifications. The treatment of the comparative that we have presented is more extensive and general than that of other NLP Systems to date, and also is simple to implement. Only a small number of productions of the BNF component were changed to cover the comparative struc- tures described in this paper. In addition, three restrictions were modified for the com- parative, and a set of separate add-on restric- tious were included to handle comparative zeroing patterns and scope marker require- ments. Special regularization procedures were written to regularize the different compara- tive forms so that the standard Montague- style compositional translation rules could be used prior to the comparative regularization phase. Although we can process many forms of the comparative, there is still substantial work that remains which involves comparative sen- tences where the comparative clause itself has been omitted, as in New York banks are start- ing to offer higher interest rates. In some cases the comparison is between two different time periods; in other cases the comparison involves different types of like objects, such as the interest rates of New York banks com- pared to the interest rates of Florida banks. The context can often be an aid in helping to recover the missing information, but the re- covery problem is still quite a challenge. Sen- tences with this type of anaphora are very in- teresting because they occur surprisingly reg- ularly in language, and yet the recovery possi- bilities are more limited and more controlled than those occurring in discourse in general. Possibly these type of sentences can provide us with clues as to what elements are significant for the recovery of the missing information. Acknowledgements I would like to thank Ralph Grishman, Naomi Sager, and Tomek Strzalkowski for their help and comments. References [1] B. BaUard. A general computational treatment of comparatives for natural language question answering. In Proc. of the ~6th Annual Meeting of the As- sociation for Computational Linguistics, pages 41-48, 1988. [21 Joan W. Bresnan. Syntax of the com- parative clause construction in English. Linguistic Inquiry, IV(3):275-343, 1973. [3] Noam Chomsky. Aspects of the Theory of Syntaz. M.I.T. Press, Cambridge, Mass., 1965. 167 [4] Noam Chomsky. On wh-movement. In P. Culicover, T. Wasow, and A. Akma- jian, editors, Formal Syntaz, pages 71- 132, Academic Press, .New York, 1977. [5] M.J. Cresswell. Logics and Language. Methuen, London, 1973. [6] M.J. Cresswell. The semantics of degree. In B.H.Partee, editor, Montague Gram- mar, pages 261-292, Academic Press, New York, 1975. [7] C. Friedman. A Computational Treat- ment of the Comparative. PhD thesis, New York University, 1989. Reprinted as PROTEUS Project Memorandum 21, New York University, Courant Insti- tute of Mathematical Science, Proteus Project, New York, 1989. [8] R. Grishman. PROTEUS Parser Refer- ence Manual. PROTEUS Project Memo- randum 4, New York University, Courant Institute of Mathematical Science, Pro- teus Project, New York, July 1986. [9] B. Grosz, D. Appelt, P. Martin, and F. Pereira. Team: an experiment in the de- sign of transportable natural-language in- terfaces. Artilical Intelligence, 32(2): 173- 243, 1987. [10] Zellig Harris. A Grammar of English On Mathematical Principles. John Wi- ley and Sons, New York, N.Y., 1982. [11] Ewan Klein. The interpretation of adjec- tival comparatives. Journal of Linguis- tics, (18):113-136, 1982. [12] Ewan Klein. A semantics for positive and comparative adjectives. Linguistics and Philosophy, (4):1-45, 1980. [13] J. Pinkham. The Formation of Compara- tive Clauses in French and English. Gar- land Publishing, New York, 1985. [14] M. Rayner and A. Banks. Parsing and in- terpreting comparatives. In Proc. of the 26th Annual Meeting of the Association for Computational Linguistics, pages 49- 60, 1988. [15] Naomi Sager. Natural Language Infor- mation Processing: A Computer Gram- mar of English and Its Applications. Addison-Wesley, Reading, Mass., 1981. [16] W.A. Woods. Semantics and quantifi- cation in natural language question an- swering systems. Advances in Comput- ers, 17:1-87, 1978. 168 . it. The scope of quantifiers under the comparative is also in- tegrated into the system in a general way. 1 Introduction Recently there has been interest in the devel- opment of a general computational. Generally, in the case of the comparative, the criteria used for determining whether or not a quantifier should have a wider scope in- volves the location of the quantifier relative to the. approach to the computational treatment of the comparative, which provides more general coverage of the comparative than that of other NLP Systems while not obscuring the underly- ing system.